White 424 vs Black 401
White starts from setup 424 (RBNQBNKR), Black from setup 401 (BRQBNNKR). In the encyclopedia since 2026-10-03: neither side starts better.
|cp| ≤ 5 at 400M · 800M · 1.6B · 4B nodes, two independent engines agree
The two setups
White: setup #424 R B N Q B N K R
King on the g-file, rooks on a, h, queen on the d-file; no bishop starts in a corner; the knights start on central files. The king already stands on a castled square, so one of the castlings moves only the rook. In ordinary symmetric play setup 424 gives White +0.23 (Morozov Balance Index, 400M nodes).
Black: setup #401 B R Q B N N K R
King on the g-file, rooks on b, h, queen on the c-file; one bishop starts in a corner; the knights start on central files. The king already stands on a castled square, so one of the castlings moves only the rook. In ordinary symmetric play setup 401 gives White -0.07 (Morozov Balance Index, 400M nodes).
Why the pair is balanced
At the deepest rungs (400M, 800M, 1.6B nodes) the evaluation never left ±1 centipawns of equality, reaching search depth 57.
Admission rule: |cp| ≤ 5 at four budgets up to 4 billion nodes, no one-sided drift along the ladder, and confirmation by two independent engines — Berserk and Lc0 — each below its own median on symmetric positions.
The shallow rungs agreed early: from 100 thousand to 128 million nodes the evaluation never left ±9 cp.
For comparison, in symmetric play setup 424 gives White +0.23 and setup 401 gives White -0.07: with both sides on the same rank the first move is worth something. In this pair Black's own setup absorbs that edge completely.
White is not forced into a single path: the best first move is d4, and 3 first moves are within 10 cp of it.
Along the engine's main line (30 moves) the largest swing was 45 cp (around move 16), ending at 0 cp — the position stays playable for both sides.
Engine self-play agrees: 10 games, White won 0, drawn 10, Black won 0 (White scored 50.0%).
Verification ladder
Nine independent searches of the starting position, each with a larger node budget. Evaluation in centipawns from White's point of view.
| Stage | Nodes | Depth | Eval, cp | Main line |
|---|---|---|---|---|
| S0 | 100 000 | 17 | -9 | 1. c3 h5 2. h4 c5 3. e4 b5 4. d4 Nd6 |
| S1 | 500 000 | 21 | +3 | 1. h4 h5 2. d4 c5 3. c3 d5 4. a4 b6 |
| S2 | 2 000 000 | 26 | +8 | 1. h4 h5 2. c3 d5 3. d4 c5 4. a4 b6 |
| S3 | 8 000 000 | 29 | +8 | 1. e4 c5 2. c3 d5 3. e5 d4 4. cxd4 b6 |
| S4 | 32 000 000 | 34 | -1 | 1. e4 b6 2. f3 d5 3. exd5 Bxd5 4. Ne3 Bb7 |
| S5 | 128 000 000 | 38 | +1 | 1. h4 h5 2. e4 b6 3. c3 d5 4. e5 d4 |
| S6 | 400 000 000 | 48 | +1 | 1. e4 c5 2. c3 b5 3. d4 h5 4. Ne3 cxd4 |
| S7 | 800 000 000 | 51 | 0 | 1. e4 c5 2. c3 b5 3. Ne3 Ng6 4. f3 h5 |
| S8 | 1 600 000 000 | 57 | 0 | 1. e4 c5 2. c3 b5 3. d4 Bb6 4. a4 bxa4 |
Deep verification
The search ladder reaches 1.6 billion nodes; admission needs a 4-billion rung and two further engines on top of that. Beyond even that, every pair was re-checked at budgets up to ten times larger and in thousands of self-play games. This section shows what each check returned for this pair.
| Nodes | Eval, cp |
|---|---|
| 4 000 000 000 | not checked |
| 8 000 000 000 | not checked |
| 16 000 000 000 | not checked |
This pair held exactly 0.00 up to 1 600 000 000 nodes.
Independent engines, run on the same position:
- Berserk 14: 0
- Lc0 0.32.1: +6
Independent confirmations: 2 of 3. An engine counts as confirming when its reading of the pair is closer to equality than its own reading of a typical symmetric Chess960 position (+10 for Berserk, +18 for Lc0). Where only one engine confirms, the pair is balanced according to that engine alone, and this page says so.
Own weight of each setup, measured against the classical array: White +72, Black +119, difference -47. A balanced pair needs White's setup to be weaker by about the price of the first move.
Extended self-play: 10 games, 0 White wins, 10 draws, 0 Black wins, White scored 50.0%.
Best first moves
The 3 best first moves for White, searched together at 400 000 000 nodes.
| # | Eval, cp | Depth | Main line |
|---|---|---|---|
| 1 | +11 | 43 | 1. d4 c5 2. c3 h5 3. h4 d5 4. f3 Bc7 5. Qd2 b6 |
| 2 | +10 | 42 | 1. h4 e5 |
| 3 | +9 | 42 | 1. c3 c5 2. d4 h5 3. e4 h4 4. h3 b5 5. Ne2 Nf6 |
Main-line play-out
30 moves, 5 000 000 nodes per half-move. Largest |evaluation| 45 cp, mean 15.8 cp, final 0 cp.
| # | White | cp | Black | cp |
|---|---|---|---|---|
| 1 | h4 | +7 | h5 | -9 |
| 2 | e4 | -9 | b6 | -7 |
| 3 | c3 | -11 | d5 | -11 |
| 4 | e5 | -8 | d4 | -13 |
| 5 | cxd4 | -14 | Qd7 | -15 |
| 6 | Ne2 | -5 | c5 | 0 |
| 7 | dxc5 | 0 | bxc5 | 0 |
| 8 | Ne3 | 0 | Bc7 | +5 |
| 9 | f4 | +15 | g6 | +25 |
| 10 | b3 | +26 | Ne6 | +17 |
| 11 | Bc2 | +16 | N8g7 | +29 |
| 12 | Rc1 | +15 | Nd4 | +25 |
| 13 | Bb1 | +28 | Rd8 | +27 |
| 14 | O-O | +23 | O-O | +24 |
| 15 | Ng3 | +30 | f5 | +39 |
| 16 | Ne2 | +41 | Nge6 | +45 |
| 17 | Rf2 | +27 | Kg7 | +26 |
| 18 | Nc4 | +22 | Qc6 | +25 |
| 19 | Rc3 | +25 | Qa6 | +24 |
| 20 | Rg3 | +26 | Nxe2+ | +20 |
| 21 | Qxe2 | +29 | Kh7 | +16 |
| 22 | Qf1 | +21 | Bc6 | +21 |
| 23 | d3 | +21 | Bd5 | +20 |
| 24 | Bd2 | +24 | Rd7 | +16 |
| 25 | Kh2 | +17 | Bxc4 | +18 |
| 26 | dxc4 | +5 | Rfd8 | 0 |
| 27 | Qd1 | 0 | Ng7 | 0 |
| 28 | Qe1 | +9 | Rxd2 | 0 |
| 29 | Rxd2 | 0 | Ba5 | 0 |
| 30 | Rgd3 | 0 | Rxd3 | 0 |
Engine self-play
10 games at 500 000 nodes per move: White won 0, drawn 10, Black won 0 — White scored 50.0%. Average length 44.1 moves.
Sample game 1 (1/2-1/2)
1. d4 b6 2. h4 h5 3. c4 e6 4. a4 Nf6 5. f3 c5 6. e4 cxd4 7. Bg3 Be7 8. Nb3 d6 9. Nxd4 Qxc4 10. Ne3 Qc8 11. O-O Qd7 12. Bd3 Ng6 13. Bb5 Qd8 14. Bc4 O-O 15. Rc1 Qd7 16. Bb5 Qd8 17. Bc4 Qd7 18. Qb3 d5 19. exd5 Bc5 20. Nxe6 fxe6 21. dxe6 Qe7 22. Kh1 Bxe3 23. Qxe3 Nd5 24. Bxd5 Bxd5 25. Bxb8 Rxb8 26. Qg5 Qxg5 27. hxg5 Bxe6 28. Rc6 Nf8 29. Re1 Bf5 30. Re7 a5 31. b3 g6 32. Kh2 Kh8 33. Kg3 Kg8 34. Kf2 Bd7 35. Rd6 Bf5 36. Rc6 Bd7 37. Rd6 Bf5
Sample game 2 (1/2-1/2)
1. d4 d5 2. c3 c5 3. h4 h5 4. a4 b6 5. f3 Bc7 6. Bg3 Rh6 7. e3 b5 8. axb5 Rxb5 9. b3 cxd4 10. Bxc7 Qxc7 11. cxd4 Rb8 12. Nd3 Rhb6 13. Nc5 Rd8 14. Qe1 e5 15. Qg3 exd4 16. exd4 a6 17. Kf2 g6 18. Ne3 Qxg3+ 19. Kxg3 Nc7 20. Bd3 Nfe6 21. Nc2 Nxc5 22. dxc5 Rxb3 23. Bxa6 Ne6 24. Rhc1 Kg7 25. Ne1 Bc6 26. Bf1 Rc8 27. Ra7 Kf6 28. Nd3 Bb7 29. Ra5 d4 30. Nf4 Rc3 31. Rd1 Rd8 32. Ne2 Rb3 33. Nf4 Rc3 34. Ne2 Rc2 35. Nf4
Play it in the CH960 app
Open this page on a phone with the CH960 app installed, or find pair 424 / 401 in the app's encyclopedia, then choose how to play.
- Local game — two players on one device, with a clock.
- With a mentor — a clearly labelled training bot with hints, at your level.
- Challenge a friend — an online game by link; both players get the same pair, colours swap on rematch.
Play this pair against the computer, right here Play a friend
FEN (Shredder, castling rights by rook files): brqbnnkr/pppppppp/8/8/8/8/PPPPPPPP/RBNQBNKR w AHbh - 0 1
Mirror twin (the same position mirrored): White 733 vs Black 747.